We develop a general equilibrium model of cryptocurrency to study a double spending prevention mechanism without payment confirmations. Agents trade cryptocurrency using a digital wallet, and the cryptocurrency system provides a means to verify a wallet's double spending history. Double spending can be prevented without payment confirmations under some conditions if a wallet has a good reputation for transaction history. As the time required for each confirmation increases, double spending incentives decrease. We provide insights into the determinants of Bitcoin transaction fees, quantitatively assess the current Bitcoin system, and evaluate the welfare gain from fast transactions without payment confirmations.